Edit Profile (opens in new tab) Cercignani, Carlo Co-Author Distance Author ID: cercignani.carlo Published as: Cercignani, Carlo; Cercignani, C. External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 205 Publications since 1962, including 15 Books 8 Contributions as Editor · 2 Further Contributions Biographic References: 7 Publications Co-Authors: 63 Co-Authors with 106 Joint Publications 1,696 Co-Co-Authors all top 5 Co-Authors 97 single-authored 14 Bobylev, Alexandre Vasiljévitch 14 Lampis, Maria 9 Illner, Reinhard 7 Kremer, Gilberto Medeiros 7 Lorenzani, Silvia 6 Martínez Gamba, Irene 5 Frezzotti, Aldo 4 Arkeryd, Leif O. 4 Majorana, Armando 4 Shinbrot, Marvin 3 Abbà, Antonella 3 Aoki, Kazuo 3 Cornille, Henri 3 Pagani, Carlo Domenico 3 Pulvirenti, Mario 3 Sgarra, Carlo 3 Valdettaro, Lorenzo 2 Bassanini, Piero 2 Biscari, Paolo 2 Fiszdon, Wladyslaw 2 Freotti, A. 2 Jerome, Joseph W. 2 Kogan, Mikhail Naumovich 2 Levermore, C. David 2 Penrose, Roger 2 Shu, Chi-Wang 2 Struckmeier, Jens 1 Akeryd, Leif 1 Albertoni, Sergio 1 Arnold, Anton 1 Arthur, M. D. 1 Batt, Jürgen 1 Battarra, Viliam 1 Bobrov, I. N. 1 Boffi, Vinicio C. 1 Bucci, Riccardo 1 Caflisch, Russel E. 1 Cannone, Marco 1 Cortese, Stefano 1 Desvillettes, Laurent 1 Ernst, Matthieu H. 1 Esposito, Raffaele 1 Gabetta, Ester 1 Gerasimenko, Viktor Ivanovich 1 Giurin, M. C. 1 Greenberg, William 1 Greppi, Mauro 1 Grosfils, Patrick 1 Guiraud, Jean-Pierre 1 Lampi, Maria 1 Lanford, Oscar E. III 1 Lebowitz, Joel Louis 1 Lentati, Andrea 1 Marra, Rossana 1 Mignemi, B. 1 Neudachin, Ilya 1 Nocilla, Silvio 1 Palczewski, Andrzej 1 Petrina, Dmitri Yakovych 1 Polewczak, Jacek 1 Protopopescu, Vladimir A. 1 Sattinger, David H. 1 Sharipov, Felix M. 1 Siewert, Charles E. 1 Slemrod, Marshall 1 Smolderen, Jean J. 1 Spohn, Herbert 1 Stoica, Cristina 1 Succi, Sauro 1 Takata, Shigeru 1 Tambi, R. 1 Tironi, Gino 1 Toscani, Giuseppe 1 Vigna, B. 1 Zweifel, Paul F. all top 5 Serials 31 Journal of Statistical Physics 23 Transport Theory and Statistical Physics 9 Physics of Fluids 7 Physics of Fluids 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Meccanica 6 Applied Mathematics Letters 4 Archive for Rational Mechanics and Analysis 4 Communications in Mathematical Physics 3 Computers & Mathematics with Applications 3 Journal of Mathematical Physics 3 Continuum Mechanics and Thermodynamics 2 Physics of Fluids, A 2 Mechanics Research Communications 2 European Journal of Mechanics. B. Fluids 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 2 Communications in Partial Differential Equations 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Applied Mathematical Sciences 2 Lecture Notes in Mathematics 2 Progress in Mathematical Physics 1 AIAA Journal 1 Archives of Mechanics 1 Computer Methods in Applied Mechanics and Engineering 1 Communications on Pure and Applied Mathematics 1 International Journal of Heat and Mass Transfer 1 Journal of Fluid Mechanics 1 Mathematical Methods in the Applied Sciences 1 Physica A 1 Atti della Accademia Peloritana dei Pericolanti. Classe di Scienze Fisiche, Matemàtiche e Naturali 1 Duke Mathematical Journal 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Rivista di Matematica della Università di Parma. Serie IV 1 Teoretichna i Prilozhna Mekhanika 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Surveys on Mathematics for Industry 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento 1 Annals of Physics 1 Atti del Seminario Matematico e Fisico dell’Università di Modena 1 Journal of Non-Equilibrium Thermodynamics 1 Journal of Physics A: Mathematical and General 1 SIAM Journal on Applied Mathematics 1 Bollettino della Unione Matemàtica Italiana. Serie VII. A 1 Engineering Analysis with Boundary Elements 1 Discrete and Continuous Dynamical Systems 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Rivista di Matematica della Università di Parma. Serie 6 1 Comptes Rendus de l’Académie des Sciences. Série II. Fascicule b. Mécanique 1 Oberwolfach Reports 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 1 Il Nuovo Cimento, X. Series 1 Istituto Lombardo, Accademia di Scienze e Lettere, Rendiconti, Sezione A 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 CISM International Centre for Mechanical Sciences. Courses and Lectures 1 DMV Seminar 1 Mathematics and its Applications (Dordrecht) 1 Studies in Statistical Mechanics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Modeling and Simulation in Science, Engineering and Technology 1 Cambridge Texts in Applied Mathematics all top 5 Fields 163 Fluid mechanics (76-XX) 129 Statistical mechanics, structure of matter (82-XX) 25 Partial differential equations (35-XX) 20 Integral equations (45-XX) 9 Numerical analysis (65-XX) 8 General and overarching topics; collections (00-XX) 8 History and biography (01-XX) 6 Classical thermodynamics, heat transfer (80-XX) 4 Mechanics of particles and systems (70-XX) 4 Quantum theory (81-XX) 3 Integral transforms, operational calculus (44-XX) 3 Probability theory and stochastic processes (60-XX) 3 Mechanics of deformable solids (74-XX) 3 Relativity and gravitational theory (83-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Optics, electromagnetic theory (78-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 160 Publications have been cited 4,134 times in 2,783 Documents Cited by ▼ Year ▼ The Boltzmann equation and its applications. Zbl 0646.76001 Cercignani, Carlo 1,005 1988 The mathematical theory of dilute gases. Zbl 0813.76001 Cercignani, Carlo; Illner, Reinhard; Pulvirenti, Mario 666 1994 Theory and application of the Boltzmann equation. Zbl 0403.76065 Cercignani, Carlo 345 1975 Rarefied gas dynamics. From basic concepts to actual calculations. Zbl 0961.76002 Cercignani, Carlo 180 2000 Mathematical methods in kinetic theory. Zbl 0191.25103 Cercignani, C. 173 1969 The relativistic Boltzmann equation: Theory and applications. Zbl 1011.76001 Cercignani, Carlo; Kremer, Gilberto Medeiros 120 2002 Kinetic models for gas-surface interactions. Zbl 0288.76041 Cercignani, C.; Lampis, M. 90 1971 Mathematical methods in kinetic theory. 2nd ed. Zbl 0726.76083 Cercignani, Carlo 86 1990 Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions. Zbl 1134.82324 Bobylev, A. V.; Cercignani, C. 53 2003 Elementary solutions of the linearized gas-dynamics Boltzmann equation and their application to the slip-flow problem. Zbl 0114.22104 Cercignani, C. 38 1962 Many-particle dynamics and kinetic equations. Zbl 0933.82001 Cercignani, C.; Gerasimenko, V. I.; Petrina, D. Ya. 35 1997 Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials. Zbl 1119.82318 Bobylev, A. V.; Cercignani, C.; Toscani, G. 33 2003 On the self-similar asymptotics for generalized nonlinear kinetic Maxwell models. Zbl 1192.35126 Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 31 2009 Measure solutions of the steady Boltzmann equation in a slab. Zbl 0733.76063 Arkeryd, Leif; Cercignani, Carlo; Illner, Reinhard 31 1991 Slow rarefied flows. Theory and application to micro-electro-mechanical systems. Zbl 1097.82001 Cercignani, Carlo 31 2006 On the Boltzmann equation for rigid spheres. Zbl 0295.76048 Cercignani, Carlo 30 1972 Moment equations for a granular material in a thermal bath. Zbl 1001.82092 Bobylev, A. V.; Cercignani, C. 28 2002 Non-existence of a steady rarefied supersonic flow in a half-space. Zbl 0449.76056 Arthur, M. D.; Cercignani, C. 27 1980 High field approximations to a Boltzmann-Poisson system and boundary conditions in a semiconductor. Zbl 0894.76072 Cercignani, C.; Gamba, I. M.; Levermore, C. D. 26 1997 Global existence of solutions for a model Boltzmann equation. Zbl 0960.82513 Cercignani, C. 26 1987 Mathematical models in rarefied gas dynamics. Zbl 0850.76620 Cercignani, C. 25 1991 A global existence theorem for the initial-boundary-value problem for the Boltzmann equation when the boundaries are not isothermal. Zbl 0789.76075 Akeryd, Leif; Cercignani, Carlo 25 1993 H-theorem and trend to equilibrium in the kinetic theory of gases. Zbl 0538.76068 Cercignani, C. 25 1982 Global existence in \(L^ 1\) for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation. Zbl 0780.76066 Arkeryd, Leif; Cercignani, Carlo 24 1990 Ludwig Boltzmann. The man who trusted atoms. Foreword by Sir Roger Penrose. Zbl 0917.01028 Cercignani, Carlo 24 1998 Shear flow of a granular material. Zbl 0990.82023 Cercignani, C. 24 2001 Device benchmark comparisons via kinetic, hydrodynamic, and high-field models. Zbl 0966.76080 Cercignani, Carlo; Gamba, Irene M.; Jerome, Joseph W.; Shu, Chi-Wang 22 2000 Monte Carlo simulation of the Taylor-Couette flow of a rarefied gas. Zbl 0785.76068 Stefanov, Stefan; Cercignani, Carlo 21 1993 Self-similar solutions of the Boltzmann equation and their applications. Zbl 1001.82091 Bobylev, A. V.; Cercignani, C. 21 2002 Nonequilibrium phenomena I: The Boltzmann equation. Zbl 0583.76004 21 1983 Half-space problems in the kinetic theory of gases. Zbl 0594.76068 Cercignani, C. 20 1986 On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation. Zbl 0688.76053 Arkeryd, Leif; Cercignani, Carlo 20 1989 The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation. Zbl 1025.44002 Bobylev, A. V.; Cercignani, C. 19 2002 Analytic solution of the temperature jump problem for the BGK model. Zbl 0376.76055 Cercignani, Carlo 18 1977 Flow of a rarefied gas past an axisymmetric body. II: Case of a sphere. Zbl 0172.54701 Cercignani, C.; Pagani, C. D.; Bassanini, P. 18 1968 On the rate of entropy production for the Boltzmann equation. Zbl 0958.82040 Bobylev, Alexander V.; Cercignani, Carlo 17 1999 Exact eternal solutions of the Boltzmann equation. Zbl 1001.82090 Bobylev, A. V.; Cercignani, C. 17 2002 On the initial-boundary value problem for the Boltzmann equation. Zbl 0753.76151 Cercignani, Carlo 16 1991 Existence of global solutions for the space inhomogeneous Enskog equation. Zbl 0629.76083 Cercignani, Carlo 16 1987 A boundary value problem for discrete-velocity models. Zbl 0647.76050 Cercignani, Carlo; Illner, Reinhard; Shinbrot, Marvin 16 1987 Rayleigh-Bénard flow of a rarefied gas and its attractors. I: Convection regime. Zbl 1185.76355 Stefanov, S.; Roussinov, V.; Cercignani, C. 16 2002 The Boltzmann equation and fluid dynamics. Zbl 1229.76093 Cercignani, C. 15 2002 A drift-collision balance for a Boltzmann–Poisson system in bounded domains. Zbl 0987.82012 Cercignani, C.; Gamba, I. M.; Levermore, C. D. 15 2001 Discrete velocity models without nonphysical invariants. Zbl 0958.82041 Bobylev, Alexander V.; Cercignani, Carlo 14 1999 Plane Poiseuille flow with symmetric and nonsymmetric gas-wall interactions. Zbl 1076.82041 Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 14 2005 On the kinetic theory of a dense gas of rough spheres. Zbl 0677.76080 Cercignani, Carlo; Lampis, Maria 14 1988 Small data existence for the Enskog equation in \(L^ 1\). Zbl 1086.82540 Cercignani, Carlo 13 1988 A remarkable estimate for the solutions of the Boltzmann equation. Zbl 0762.35090 Cercignani, Carlo 13 1992 A boundary value problem for the two dimensional Broadwell model. Zbl 0668.76091 Cercignani, Carlo; Illner, Reinhard; Shinbrot, Marvin 13 1988 Existence of homoenergetic affine flows for the Boltzmann equation. Zbl 0697.76089 Cercignani, Carlo 13 1989 Generalized kinetic Maxwell type models of granular gases. Zbl 1298.76209 Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 13 2008 On nonlinear stationary half-space problems in discrete kinetic theory. Zbl 1084.82561 Cercignani, Carlo; Illner, Reinhard; Pulvirenti, Mario; Shinbrot, Marvin 12 1988 Scaling limits and models in physical processes. Zbl 0912.35149 Cercignani, Carlo; Sattinger, David H. 12 1998 Shock waves for a discrete velocity gas mixture. Zbl 0972.82072 Cercignani, Carlo; Cornille, Henri 12 2000 Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions. Zbl 0937.45007 Cercignani, C.; Illner, R. 12 1996 Global weak solutions of the Boltzmann equation. Zbl 1097.82022 Cercignani, Carlo 12 2005 The grad limit for a system of soft spheres. Zbl 0505.76088 Cercignani, Carlo 12 1983 On diffusive equilibria in generalized kinetic theory. Zbl 1051.82021 Cercignani, Carlo; Illner, Reinhard; Stoica, Cristina 12 2001 The Milne problem with a force term. Zbl 0899.76319 Cercignani, C.; Marra, R.; Esposito, R. 12 1998 Gaseous mixture slit flow at intermediate Knudsen numbers. Zbl 0767.76064 Cercignani, Carlo; Sharipov, Felix 11 1992 The Boltzmann equation and high altitude aerodynamics. Zbl 1112.76447 Cercignani, Carlo 11 1997 Kinetic theories and the Boltzmann equation. Lectures given at the 1st 1981 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), Held at Montecatini, Italy, June 10-18, 1981. Zbl 0536.00019 11 1984 The structure of an infinitely strong shock wave. Zbl 1149.76336 Cercignani, Carlo; Frezzotti, Aldo; Grosfils, Patrick 11 1999 Monte Carlo simulation of Bénard’s instability in a rarefied gas. Zbl 0764.76060 Stefanov, S.; Cercignani, C. 10 1992 On the thermodynamics of a discrete velocity gas. Zbl 0811.76078 Cercignani, Carlo 10 1994 Weak solutions of the Boltzmann equation and energy conservation. Zbl 0830.35107 Cercignani, C. 10 1995 Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules. Zbl 1190.76022 Cercignani, Carlo; Lorenzani, Silvia 10 2010 Discrete velocity models for mixtures. Zbl 0917.76075 Bobylev, Alexander V.; Cercignani, Carlo 9 1998 Variational approach to gas flows in microchannels. Zbl 1187.76086 Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 9 2004 Equilibrium states and trend to equilibrium in a gas according to the Boltzmann equation. Zbl 0723.76079 Cercignani, C. 9 1990 A new scattering kernel in kinetic theory of gases. Zbl 0874.76076 Cercignani, Carlo; Lampis, Maria; Lentati, Andrea 8 1995 Steady solutions of the nonlinear Boltzmann equation. Zbl 0914.76071 Cercignani, Carlo 8 1998 The Boltzmann equation approach to the shear flow of a granular material. Zbl 1001.76092 Cercignani, Carlo 8 2002 Are there more than five linearly-independent collision invariants for the Boltzmann equation? Zbl 0718.60113 Cercignani, Carlo 8 1990 Ludwig Boltzmann. The man who trusted atoms. Foreword by Sir Roger Penrose. Zbl 1095.01502 Cercignani, Carlo 8 2006 Plane Poiseuille-Couette problem in micro-electro-mechanical systems applications with gas-rarefaction effects. Zbl 1262.76087 Cercignani, Carlo; Lampi, Maria; Lorenzani, Silvia 8 2006 Flow of a rarefied gas past an axisymmetric body. I: General remarks. Zbl 0172.54602 Cercignani, C.; Pagani, C. D. 8 1968 Stokes paradox in kinetic theory. Zbl 0155.55503 Cercignani, C. 8 1968 Analysis of subgrid scale models. Zbl 1100.76527 Abbà, A.; Cercignani, C.; Valdettaro, L. 7 2003 Rayleigh-Bénard flow of a rarefied gas and its attractors. II: Cchaotic and periodic convective regimes. Zbl 1185.76356 Stefanov, S.; Roussinov, V.; Cercignani, C. 7 2002 Analysis of thermal, sound, and shear waves according to a relativistic kinetic model. Zbl 0603.76128 Cercignani, Carlo; Majorana, Armando 7 1985 Moment closure of the relativistic Anderson and Witting model equation. Zbl 0971.82516 Cercignani, C.; Kremer, G. M. 7 2001 A trace theorem in kinetic theory. Zbl 0744.45005 Cannone, Marco; Cercignani, Carlo 6 1991 On relativistic collisional invariants. Zbl 0964.82046 Cercignani, C.; Kremer, G. M. 6 1999 Monte Carlo simulation of a channel flow of a rarefied gas. Zbl 0799.76065 Stefanov, Stefan; Cercignani, Carlo 6 1994 Kinetic theory with “bounce-back” boundary conditions. Zbl 0675.76081 Cercignani, Carlo 6 1989 A sketch of the theory of the Boltzmann equation. Zbl 0465.76068 Cercignani, Carlo 6 1978 The paradox of the inverted temperature profiles between an evaporating and a condensing surface. Zbl 0586.76132 Cercignani, C.; Fiszdon, W.; Freotti, A. 6 1985 Sur des critères d’existence globale en théorie cinétique discrète. (On some criteria of global existence in discrete kinetic theory). Zbl 0622.76080 Cercignani, Carlo 6 1985 On a functional equation arising in the kinetic theory of gases. Zbl 0703.76062 Arkeryd, Leif; Cercignani, Carlo 6 1990 Bifurcation problems in fluid-mechanics. Zbl 0195.27401 Cercignani, Carlo 6 1970 New scattering kernel for gas-surface interaction. Zbl 0892.76076 Cercignani, C.; Lampis, M. 5 1997 Temperature, entropy, and kinetic theory. Zbl 0945.82553 Cercignani, Carlo 5 1997 Measure solutions for the steady linear Boltzmann equation in a slab. Zbl 0940.35165 Cercignani, C.; Giurin, M. C. 5 1999 Errata: Weak solutions of the Boltzmann equation and energy conservation. Zbl 0841.35093 Cercignani, C. 5 1995 Bénard’s instability in kinetic theory. Zbl 0793.76042 Cercignani, Carlo; Stefanov, Stefan 5 1992 Validation of a Monte Carlo simulation of the plane Couette flow of a rarefied gas. Zbl 0834.76066 Cercignani, Carlo; Cortese, Stefano 5 1994 On partial indices for a matrix Riemann-Hilbert problem. Zbl 0483.76090 Cercignani, C.; Siewert, C. E. 5 1982 Rarefied gas flow through long slots. Zbl 0422.76045 Cercignani, Carlo; Neudachin, Ilya 5 1979 Existence and uniqueness for nonlinear boundary value problems in kinetic theory. Zbl 0681.76076 Cercignani, Carlo; Palczewski, Andrzej 5 1987 Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules. Zbl 1190.76022 Cercignani, Carlo; Lorenzani, Silvia 10 2010 On the self-similar asymptotics for generalized nonlinear kinetic Maxwell models. Zbl 1192.35126 Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 31 2009 Generalized kinetic Maxwell type models of granular gases. Zbl 1298.76209 Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 13 2008 134 years of Boltzmann equation. Zbl 1156.82301 Cercignani, Carlo 3 2008 BEM approaches and simplified kinetic models for the analysis of damping in deformable MEMS. Zbl 1195.76276 Cercignani, C.; Frangi, A.; Lorenzani, S.; Vigna, B. 4 2007 Rayleigh-Bénard flow of a rarefied gas and its attractors. III: Three-dimensional computer simulations. Zbl 1182.76719 Stefanov, S.; Roussinov, V.; Cercignani, C. 3 2007 Transport phenomena and kinetic theory. Applications to gases, semiconductors, photons, and biological systems. Zbl 1109.82001 2 2007 On the Reynolds equation for linearized models of the Boltzmann operator. Zbl 1136.82018 Cercignani, C.; Lampis, M.; Lorenzani, S. 2 2007 Slow rarefied flows. Theory and application to micro-electro-mechanical systems. Zbl 1097.82001 Cercignani, Carlo 31 2006 Ludwig Boltzmann. The man who trusted atoms. Foreword by Sir Roger Penrose. Zbl 1095.01502 Cercignani, Carlo 8 2006 Plane Poiseuille-Couette problem in micro-electro-mechanical systems applications with gas-rarefaction effects. Zbl 1262.76087 Cercignani, Carlo; Lampi, Maria; Lorenzani, Silvia 8 2006 Weak solutions of the Boltzmann equation without angle cutoff. Zbl 1108.82037 Cercignani, Carlo 2 2006 Estimating the solutions of the Boltzmann equation. Zbl 1110.82036 Cercignani, Carlo 1 2006 Plane Poiseuille flow with symmetric and nonsymmetric gas-wall interactions. Zbl 1076.82041 Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 14 2005 Global weak solutions of the Boltzmann equation. Zbl 1097.82022 Cercignani, Carlo 12 2005 Variational approach to gas flows in microchannels. Zbl 1187.76086 Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 9 2004 Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions. Zbl 1134.82324 Bobylev, A. V.; Cercignani, C. 53 2003 Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials. Zbl 1119.82318 Bobylev, A. V.; Cercignani, C.; Toscani, G. 33 2003 Analysis of subgrid scale models. Zbl 1100.76527 Abbà, A.; Cercignani, C.; Valdettaro, L. 7 2003 Variational approach to plane Poiseuille flow with general boundary conditions. Zbl 1182.76945 Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 3 2003 Recent results in the kinetic theory of granular materials. Zbl 1255.76141 Cercignani, Carlo 3 2003 The relativistic Boltzmann equation: Theory and applications. Zbl 1011.76001 Cercignani, Carlo; Kremer, Gilberto Medeiros 120 2002 Moment equations for a granular material in a thermal bath. Zbl 1001.82092 Bobylev, A. V.; Cercignani, C. 28 2002 Self-similar solutions of the Boltzmann equation and their applications. Zbl 1001.82091 Bobylev, A. V.; Cercignani, C. 21 2002 The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation. Zbl 1025.44002 Bobylev, A. V.; Cercignani, C. 19 2002 Exact eternal solutions of the Boltzmann equation. Zbl 1001.82090 Bobylev, A. V.; Cercignani, C. 17 2002 Rayleigh-Bénard flow of a rarefied gas and its attractors. I: Convection regime. Zbl 1185.76355 Stefanov, S.; Roussinov, V.; Cercignani, C. 16 2002 The Boltzmann equation and fluid dynamics. Zbl 1229.76093 Cercignani, C. 15 2002 The Boltzmann equation approach to the shear flow of a granular material. Zbl 1001.76092 Cercignani, Carlo 8 2002 Rayleigh-Bénard flow of a rarefied gas and its attractors. II: Cchaotic and periodic convective regimes. Zbl 1185.76356 Stefanov, S.; Roussinov, V.; Cercignani, C. 7 2002 Self-similar solutions of the Boltzmann equation for non-Maxwell molecules. Zbl 1034.82046 Bobylev, A. V.; Cercignani, C. 2 2002 Shear flow of a granular material. Zbl 0990.82023 Cercignani, C. 24 2001 A drift-collision balance for a Boltzmann–Poisson system in bounded domains. Zbl 0987.82012 Cercignani, C.; Gamba, I. M.; Levermore, C. D. 15 2001 On diffusive equilibria in generalized kinetic theory. Zbl 1051.82021 Cercignani, Carlo; Illner, Reinhard; Stoica, Cristina 12 2001 Moment closure of the relativistic Anderson and Witting model equation. Zbl 0971.82516 Cercignani, C.; Kremer, G. M. 7 2001 Large size planar discrete velocity models for gas mixtures. Zbl 0995.82512 Cornille, Henri; Cercignani, Carlo 4 2001 Dispersion and absorption of plane harmonic waves in a relativistic gas. Zbl 1100.76560 Cercignani, C.; Kremer, G. M. 1 2001 Rarefied gas dynamics. From basic concepts to actual calculations. Zbl 0961.76002 Cercignani, Carlo 180 2000 Device benchmark comparisons via kinetic, hydrodynamic, and high-field models. Zbl 0966.76080 Cercignani, Carlo; Gamba, Irene M.; Jerome, Joseph W.; Shu, Chi-Wang 22 2000 Shock waves for a discrete velocity gas mixture. Zbl 0972.82072 Cercignani, Carlo; Cornille, Henri 12 2000 A domain decomposition method for Silicon devices. Zbl 1028.82021 Cercignani, Carlo; Gamba, Irene M.; Jerome, Joseph W.; Shu, Chi-Wang 5 2000 A class of planar discrete velocity models for gas mixtures. Zbl 0959.82023 Cornille, Henri; Cercignani, Carlo 4 2000 Propagation phenomena in classical and relativistic rarefied gases. Zbl 1017.82043 Cercignani, Carlo 4 2000 Trend to equilibrium of a degenerate relativistic gas. Zbl 0958.82042 Cercignani, C.; Kremer, G. M. 3 2000 The velocity distribution function in an infinitely strong shock wave. Zbl 1184.76541 Takata, Shigeru; Aoki, Kazuo; Cercignani, Carlo 2 2000 Time-derivatives and frame-invariance beyond Newtonian fluids. Zbl 1004.76073 Biscari, Paolo; Cercignani, Carlo; Slemrod, Marshall 2 2000 Applications of a new model for the differential cross-section of a classical polyatomic gas. Zbl 0990.82024 Cercignani, Carlo; Lampis, Maria; Struckmeier, Jens 1 2000 On the rate of entropy production for the Boltzmann equation. Zbl 0958.82040 Bobylev, Alexander V.; Cercignani, Carlo 17 1999 Discrete velocity models without nonphysical invariants. Zbl 0958.82041 Bobylev, Alexander V.; Cercignani, Carlo 14 1999 The structure of an infinitely strong shock wave. Zbl 1149.76336 Cercignani, Carlo; Frezzotti, Aldo; Grosfils, Patrick 11 1999 On relativistic collisional invariants. Zbl 0964.82046 Cercignani, C.; Kremer, G. M. 6 1999 Measure solutions for the steady linear Boltzmann equation in a slab. Zbl 0940.35165 Cercignani, C.; Giurin, M. C. 5 1999 A new model for the boundary conditions of the Boltzmann equation. Zbl 0978.76080 Cercignani, Carlo; Lampis, Maria 3 1999 Ludwig Boltzmann. The man who trusted atoms. Foreword by Sir Roger Penrose. Zbl 0917.01028 Cercignani, Carlo 24 1998 Scaling limits and models in physical processes. Zbl 0912.35149 Cercignani, Carlo; Sattinger, David H. 12 1998 The Milne problem with a force term. Zbl 0899.76319 Cercignani, C.; Marra, R.; Esposito, R. 12 1998 Discrete velocity models for mixtures. Zbl 0917.76075 Bobylev, Alexander V.; Cercignani, Carlo 9 1998 Steady solutions of the nonlinear Boltzmann equation. Zbl 0914.76071 Cercignani, Carlo 8 1998 Measure solutions for the steady nonlinear Boltzmann equation in a slab. Zbl 0920.35156 Cercignani, Carlo 3 1998 New models for the differential cross-section of a polyatomic gas in the frame of the scattering kernel theory. Zbl 0964.76079 Cercignani, Carlo; Lampis, Maria; Struckmeier, J. 2 1998 Monte Carlo simulation of the propagation of a disturbance in the channel flow of a rarefied gas. Zbl 0911.76070 Stefanov, S.; Cercignani, C. 2 1998 Anisotropy effects in LES simulation of turbulent flows. Zbl 0928.76052 Abbà, A.; Cercignani, C.; Valdettaro, L. 1 1998 Many-particle dynamics and kinetic equations. Zbl 0933.82001 Cercignani, C.; Gerasimenko, V. I.; Petrina, D. Ya. 35 1997 High field approximations to a Boltzmann-Poisson system and boundary conditions in a semiconductor. Zbl 0894.76072 Cercignani, C.; Gamba, I. M.; Levermore, C. D. 26 1997 The Boltzmann equation and high altitude aerodynamics. Zbl 1112.76447 Cercignani, Carlo 11 1997 New scattering kernel for gas-surface interaction. Zbl 0892.76076 Cercignani, C.; Lampis, M. 5 1997 Temperature, entropy, and kinetic theory. Zbl 0945.82553 Cercignani, Carlo 5 1997 Stress and heat flux in non-inertial reference frames. Zbl 0891.76077 Biscari, Paolo; Cercignani, Carlo 4 1997 Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions. Zbl 0937.45007 Cercignani, C.; Illner, R. 12 1996 Initial-boundary value problems for the Boltzmann equation. Zbl 0895.76082 Cercignani, Carlo 1 1996 Weak solutions of the Boltzmann equation and energy conservation. Zbl 0830.35107 Cercignani, C. 10 1995 A new scattering kernel in kinetic theory of gases. Zbl 0874.76076 Cercignani, Carlo; Lampis, Maria; Lentati, Andrea 8 1995 Errata: Weak solutions of the Boltzmann equation and energy conservation. Zbl 0841.35093 Cercignani, C. 5 1995 Interaction of evaporating and condensing particles in the free-molecular regime. Zbl 1027.76643 Kogan, M. N.; Bobrov, I. N.; Cercignani, C.; Frezzotti, A. 3 1995 On global existence theorems for the initial-boundary value problem for the Boltzmann equation. Zbl 0938.76095 Cercignani, Carlo 1 1995 The mathematical theory of dilute gases. Zbl 0813.76001 Cercignani, Carlo; Illner, Reinhard; Pulvirenti, Mario 666 1994 On the thermodynamics of a discrete velocity gas. Zbl 0811.76078 Cercignani, Carlo 10 1994 Monte Carlo simulation of a channel flow of a rarefied gas. Zbl 0799.76065 Stefanov, Stefan; Cercignani, Carlo 6 1994 Validation of a Monte Carlo simulation of the plane Couette flow of a rarefied gas. Zbl 0834.76066 Cercignani, Carlo; Cortese, Stefano 5 1994 An explicitly solvable kinetic model for semiconductors. Zbl 0839.76075 Cercignani, Carlo 4 1994 Mathematical problems in the gas dynamics of high-altitude flight. Zbl 0852.76081 Cercignani, C. 3 1994 A global existence theorem for the initial-boundary-value problem for the Boltzmann equation when the boundaries are not isothermal. Zbl 0789.76075 Akeryd, Leif; Cercignani, Carlo 25 1993 Monte Carlo simulation of the Taylor-Couette flow of a rarefied gas. Zbl 0785.76068 Stefanov, Stefan; Cercignani, Carlo 21 1993 Exact solutions of the Boltzmann equation. Zbl 0803.35151 Cercignani, C. 4 1993 On the absence of motion in certain nonequilibrium states of gases and vapors in free-molecular regime: General considerations and pipe flow. Zbl 0795.76070 Cercignani, Carlo; Frezzotti, Aldo; Kogan, Mikhail N. 1 1993 A remarkable estimate for the solutions of the Boltzmann equation. Zbl 0762.35090 Cercignani, Carlo 13 1992 Gaseous mixture slit flow at intermediate Knudsen numbers. Zbl 0767.76064 Cercignani, Carlo; Sharipov, Felix 11 1992 Monte Carlo simulation of Bénard’s instability in a rarefied gas. Zbl 0764.76060 Stefanov, S.; Cercignani, C. 10 1992 Bénard’s instability in kinetic theory. Zbl 0793.76042 Cercignani, Carlo; Stefanov, Stefan 5 1992 Half-range completeness for the Fokker-Planck equation with an external force. Zbl 0925.60060 Cercignani, C.; Sgarra, C. 4 1992 Measure solutions of the steady Boltzmann equation in a slab. Zbl 0733.76063 Arkeryd, Leif; Cercignani, Carlo; Illner, Reinhard 31 1991 Mathematical models in rarefied gas dynamics. Zbl 0850.76620 Cercignani, C. 25 1991 On the initial-boundary value problem for the Boltzmann equation. Zbl 0753.76151 Cercignani, Carlo 16 1991 A trace theorem in kinetic theory. Zbl 0744.45005 Cannone, Marco; Cercignani, Carlo 6 1991 Mathematical methods in kinetic theory. 2nd ed. Zbl 0726.76083 Cercignani, Carlo 86 1990 Global existence in \(L^ 1\) for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation. Zbl 0780.76066 Arkeryd, Leif; Cercignani, Carlo 24 1990 Equilibrium states and trend to equilibrium in a gas according to the Boltzmann equation. Zbl 0723.76079 Cercignani, C. 9 1990 Are there more than five linearly-independent collision invariants for the Boltzmann equation? Zbl 0718.60113 Cercignani, Carlo 8 1990 On a functional equation arising in the kinetic theory of gases. Zbl 0703.76062 Arkeryd, Leif; Cercignani, Carlo 6 1990 On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation. Zbl 0688.76053 Arkeryd, Leif; Cercignani, Carlo 20 1989 ...and 60 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,495 Authors 76 Cercignani, Carlo 48 Toscani, Giuseppe 37 Aoki, Kazuo 33 Pareschi, Lorenzo 33 Yang, Tong 32 Dimarco, Giacomo 32 Yun, Seok-Bae 31 Spiga, Giampiero 30 Bisi, Marzia 30 Takata, Shigeru 28 Degond, Pierre 28 Siewert, Charles E. 27 Martínez Gamba, Irene 27 Kremer, Gilberto Medeiros 26 Yushkanov, Aleksandr Alekseevich 25 Desvillettes, Laurent 25 Duan, Renjun 25 Golse, François 25 Khachatryan, Khachatur Aghavardovich 24 Bobylev, Alexandre Vasiljévitch 24 Sharipov, Felix M. 22 Carrillo de la Plata, José Antonio 22 Pulvirenti, Mario 22 Sone, Yoshio 21 Groppi, Maria 21 Latyshev, Anatolii Vasil’evich 21 Mouhot, Clément 21 Saint-Raymond, Laure 20 Klar, Axel 20 Torrilhon, Manuel 19 Arkeryd, Leif O. 19 Guo, Yan 19 Hu, Jingwei 18 Liu, Shuangqian 18 Zhang, Xianwen 18 Zhao, Huijiang 17 Esposito, Raffaele 17 Frezzotti, Aldo 17 Illner, Reinhard 17 Wagner, Wolfgang 17 Zanella, Mattia 16 Simonella, Sergio 15 Marra, Rossana 15 Struchtrup, Henning 14 Bellomo, Nicola 14 Carlen, Eric Anders 14 Shu, Chi-Wang 14 Soares, Ana Jacinta 14 Valougeorgis, Dimitris 14 Van der Mee, Cornelis Victor Maria 13 Briant, Marc 13 Gallagher, Isabelle 13 Gibelli, Livio 13 Gordevs’kyĭ, Vyacheslav Dmytrovych 13 Hauck, Cory D. 13 Jin, Shi 13 Kim, Chanwoo 13 Lebowitz, Joel Louis 13 Majorana, Armando 13 Perthame, Benoît 13 Rey, Thomas 13 Strain, Robert M. 13 Vedenyapin, Victor V. 12 Bernhoff, Niclas 12 Greenberg, William 12 Ha, Seung-Yeal 12 Li, Zhihui 12 Lods, Bertrand 12 Mieussens, Luc 12 Nouri, Anne 12 Reese, Jason M. 12 Wu, Lei 12 Wu, Lei 12 Zhang, Yonghao 11 Bodineau, Thierry 11 Garcia, Roberto D. M. 11 Lorenzani, Silvia 11 Loyalka, S. K. 11 Martalò, Giorgio 11 Mischler, Stéphane 11 Morimoto, Yoshinori 11 Ruggeri, Tommaso 11 Russo, Giovanni 11 Santos, Andrés 11 Wennberg, Bernt 11 Yu, Hongjun 11 Yu, Shih-Hsien 10 Brull, Stephane 10 Emerson, David R. 10 Filbet, Francis 10 García-Perciante, Ana Laura 10 Hadjiconstantinou, Nicolas G. 10 Jiang, Ning 10 Khachatryan, Aghavard Khachaturovich 10 Kosuge, Shingo 10 Lachowicz, Mirosław 10 Lampis, Maria 10 Nota, Alessia 10 Ohwada, Taku 10 Polewczak, Jacek ...and 2,395 more Authors all top 5 Cited in 328 Serials 246 Journal of Statistical Physics 199 Journal of Computational Physics 119 Transport Theory and Statistical Physics 103 Physics of Fluids 89 Archive for Rational Mechanics and Analysis 84 Kinetic and Related Models 67 Journal of Differential Equations 65 Journal of Fluid Mechanics 63 Communications in Mathematical Physics 60 European Journal of Mechanics. B. Fluids 53 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 52 Physica A 48 Journal of Mathematical Analysis and Applications 46 Computers and Fluids 46 Journal of Mathematical Physics 45 Computers & Mathematics with Applications 44 ZAMP. Zeitschrift für angewandte Mathematik und Physik 38 Fluid Dynamics 37 Theoretical and Mathematical Physics 35 Mathematical Methods in the Applied Sciences 35 SIAM Journal on Mathematical Analysis 33 Continuum Mechanics and Thermodynamics 27 Journal of Statistical Mechanics: Theory and Experiment 25 Physica D 25 Journal of Scientific Computing 21 Communications on Pure and Applied Mathematics 21 Computational Mathematics and Mathematical Physics 19 Applied Mathematics Letters 18 Meccanica 18 Multiscale Modeling & Simulation 17 Communications in Partial Differential Equations 16 Applied Mathematics and Computation 15 Journal of Functional Analysis 14 Journal of Computational and Applied Mathematics 14 Mathematical and Computer Modelling 13 Computer Methods in Applied Mechanics and Engineering 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 13 Annals of Physics 13 SIAM Journal on Scientific Computing 12 Computer Physics Communications 12 Stochastic Processes and their Applications 11 Physics of Fluids 11 Physics Letters. A 11 Physics of Fluids, A 11 Quarterly of Applied Mathematics 11 SIAM Journal on Numerical Analysis 11 Journal of Physics A: Mathematical and Theoretical 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 The Annals of Applied Probability 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 10 Nonlinear Analysis. Real World Applications 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Physics Reports 9 Mathematics of Computation 9 Acta Applicandae Mathematicae 9 International Journal of Computational Fluid Dynamics 8 Discrete and Continuous Dynamical Systems 8 Foundations of Physics 8 Communications in Computational Physics 7 Applicable Analysis 7 Classical and Quantum Gravity 7 General Relativity and Gravitation 7 Journal of Mathematical Biology 7 Ukrainian Mathematical Journal 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Inventiones Mathematicae 7 Mathematics and Computers in Simulation 7 Applied Mathematical Modelling 7 SIAM Journal on Applied Mathematics 7 Journal of Nonlinear Science 7 Doklady Mathematics 7 Matematicheskoe Modelirovanie 7 Nonlinear Analysis. Theory, Methods & Applications 7 Journal of Computational and Theoretical Transport 6 International Journal of Engineering Science 6 International Journal of Heat and Mass Transfer 6 International Journal for Numerical Methods in Fluids 6 Mathematical Notes 6 Advances in Mathematics 6 Probability Theory and Related Fields 6 Bulletin of the American Mathematical Society. New Series 6 Acta Mathematica Scientia. Series B. (English Edition) 6 Science China. Mathematics 6 Annals of PDE 6 Séminaire Laurent Schwartz. EDP et Applications 6 SN Partial Differential Equations and Applications 5 Acta Mechanica 5 Journal of Applied Mathematics and Mechanics 5 Nonlinearity 5 Physics Letters. B 5 Rendiconti del Seminario Matemàtico e Fisico di Milano 5 Siberian Mathematical Journal 5 Abstract and Applied Analysis 5 Communications in Nonlinear Science and Numerical Simulation 5 Communications on Pure and Applied Analysis 5 SIAM/ASA Journal on Uncertainty Quantification 4 Reports on Mathematical Physics 4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 4 Bulletin of Mathematical Biology 4 Integral Equations and Operator Theory ...and 228 more Serials all top 5 Cited in 50 Fields 1,670 Fluid mechanics (76-XX) 1,443 Statistical mechanics, structure of matter (82-XX) 1,085 Partial differential equations (35-XX) 397 Numerical analysis (65-XX) 175 Integral equations (45-XX) 150 Probability theory and stochastic processes (60-XX) 142 Classical thermodynamics, heat transfer (80-XX) 96 Biology and other natural sciences (92-XX) 85 Quantum theory (81-XX) 82 Relativity and gravitational theory (83-XX) 69 Operator theory (47-XX) 55 Mechanics of deformable solids (74-XX) 49 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 44 Ordinary differential equations (34-XX) 43 Dynamical systems and ergodic theory (37-XX) 42 Optics, electromagnetic theory (78-XX) 26 Mechanics of particles and systems (70-XX) 25 Operations research, mathematical programming (90-XX) 24 Astronomy and astrophysics (85-XX) 19 Functional analysis (46-XX) 19 Computer science (68-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 18 Statistics (62-XX) 15 Information and communication theory, circuits (94-XX) 14 Integral transforms, operational calculus (44-XX) 13 Systems theory; control (93-XX) 11 Real functions (26-XX) 10 Approximations and expansions (41-XX) 9 General and overarching topics; collections (00-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 8 Special functions (33-XX) 8 Difference and functional equations (39-XX) 8 Differential geometry (53-XX) 6 History and biography (01-XX) 4 Measure and integration (28-XX) 4 Geophysics (86-XX) 3 Algebraic geometry (14-XX) 3 Functions of a complex variable (30-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Mathematical logic and foundations (03-XX) 2 Nonassociative rings and algebras (17-XX) 2 Several complex variables and analytic spaces (32-XX) 2 General topology (54-XX) 1 Number theory (11-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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